The time fractional diffusion equation is obtained from the standard diffusion e quation by replacing the first-order time derivative with a fractional derivative of order beta is an element of (0, 1). From a physical view-point thi s generalized diffusion equation is obtained from a fractional Fick law which describes transport processes with long memory. The fundamental solution f or the Cauchy problem is interpreted as a probability density of a self-similar non-Markovian stochastic process related to a phenomenon of slow an omalous diffusion. By adopting a suitable finite-difference scheme of solution, we generate discrete models of random walk suitable for simu lating random variables whose spatial probability density evolves in time according to this fractional diffusion equation.
Time fractional diffusion: a discrete random walk approach
2002
Abstract
The time fractional diffusion equation is obtained from the standard diffusion e quation by replacing the first-order time derivative with a fractional derivative of order beta is an element of (0, 1). From a physical view-point thi s generalized diffusion equation is obtained from a fractional Fick law which describes transport processes with long memory. The fundamental solution f or the Cauchy problem is interpreted as a probability density of a self-similar non-Markovian stochastic process related to a phenomenon of slow an omalous diffusion. By adopting a suitable finite-difference scheme of solution, we generate discrete models of random walk suitable for simu lating random variables whose spatial probability density evolves in time according to this fractional diffusion equation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
